Is there a way to overlay two similar UV islands with identical vertex count?
Automatically unwrapping  identical geometry pieces one by one should produce identical UV layouts.
I.e. if you have a row of identical parts of geometry, select one, do unwrap, select another, etc. Selecting all at once may produce alike, but different islands.

If geometry is not identical, I'm afraid you're stuck with manually scaling down to zero required vertexes.